Alternating Current
Q. In an RLC series circuit, what is the condition for resonance?
A.
XL = XC
B.
R = 0
C.
XL > XC
D.
R > XL
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Solution
Resonance in an RLC series circuit occurs when the inductive reactance (X_L) equals the capacitive reactance (X_C), i.e., X_L = X_C.
Correct Answer: A — XL = XC
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Q. The power factor of an AC circuit is defined as the ratio of:
A.
Real power to apparent power
B.
Apparent power to real power
C.
Voltage to current
D.
Current to voltage
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Solution
The power factor is defined as the ratio of real power to apparent power.
Correct Answer: A — Real power to apparent power
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Q. What is the average power consumed in an AC circuit with a power factor of 0.8 and an RMS voltage of 100 V with a current of 5 A?
A.
200 W
B.
400 W
C.
300 W
D.
500 W
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Solution
Average power (P) is given by P = V_rms * I_rms * PF. Therefore, P = 100 V * 5 A * 0.8 = 400 W.
Correct Answer: C — 300 W
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Q. What is the average power consumed in an AC circuit with a power factor of 0.8 and a maximum power of 100 W?
A.
80 W
B.
100 W
C.
120 W
D.
160 W
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Solution
Average power (P_avg) is given by P_avg = P_max × power factor. Therefore, P_avg = 100 W × 0.8 = 80 W.
Correct Answer: A — 80 W
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Q. What is the effect of increasing the capacitance in a capacitor in an AC circuit on the current?
A.
Increases current
B.
Decreases current
C.
No effect
D.
Current becomes zero
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Solution
Increasing the capacitance (C) decreases the capacitive reactance (X_C), which increases the current (I) in the circuit.
Correct Answer: A — Increases current
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Q. What is the effect of increasing the capacitance in an AC circuit on the capacitive reactance?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Capacitive reactance (X_C) is given by X_C = 1/(2πfC). Increasing capacitance (C) decreases X_C.
Correct Answer: B — Decreases
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Q. What is the effect of increasing the capacitance in an AC circuit on the phase angle between voltage and current?
A.
Increases phase angle
B.
Decreases phase angle
C.
No effect
D.
Phase angle becomes 90 degrees
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Solution
Increasing capacitance decreases the phase angle between voltage and current in an AC circuit.
Correct Answer: B — Decreases phase angle
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Q. What is the effect of increasing the frequency on the capacitive reactance?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
Capacitive reactance X_C = 1/(ωC) decreases with increasing frequency.
Correct Answer: B — Decreases
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Q. What is the effect of increasing the frequency on the impedance of a series RLC circuit?
A.
Increases
B.
Decreases
C.
Remains constant
D.
Depends on R, L, and C
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Solution
The impedance (Z) of a series RLC circuit depends on the values of resistance (R), inductance (L), capacitance (C), and frequency (f). As frequency increases, the inductive reactance increases and capacitive reactance decreases, affecting the total impedance.
Correct Answer: D — Depends on R, L, and C
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Q. What is the effect of increasing the frequency on the impedance of an inductor?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
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Solution
The impedance of an inductor (Z_L) increases with frequency, as Z_L = jωL, where ω = 2πf.
Correct Answer: A — Increases
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Q. What is the effect of increasing the resistance in a series AC circuit?
A.
Increases current
B.
Decreases current
C.
No effect
D.
Increases voltage
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Solution
Increasing the resistance in a series AC circuit decreases the current.
Correct Answer: B — Decreases current
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Q. What is the effect of increasing the resistance in a series RLC circuit on the Q factor?
A.
Increases Q factor
B.
Decreases Q factor
C.
No effect
D.
Doubles Q factor
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Solution
Increasing resistance decreases the Q factor, which is defined as Q = ωL/R.
Correct Answer: B — Decreases Q factor
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Q. What is the effect of increasing the resistance in an AC circuit on the overall current?
A.
Increases current
B.
Decreases current
C.
No effect
D.
Doubles current
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Solution
According to Ohm's law, increasing resistance in an AC circuit decreases the overall current.
Correct Answer: B — Decreases current
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Q. What is the formula for calculating the total power in a series RLC circuit?
A.
P = VI
B.
P = I^2R
C.
P = V^2/R
D.
P = VI cos(φ)
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Solution
The total power in a series RLC circuit is given by P = VI cos(φ), where φ is the phase angle.
Correct Answer: D — P = VI cos(φ)
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Q. What is the formula for calculating the total power in an AC circuit with a power factor?
A.
P = VI
B.
P = VI cos(φ)
C.
P = VI sin(φ)
D.
P = V^2/R
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Solution
The total power in an AC circuit is given by P = VI cos(φ), where φ is the phase angle.
Correct Answer: B — P = VI cos(φ)
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Q. What is the formula for the total power in a series RLC circuit?
A.
P = VI
B.
P = I^2R
C.
P = V^2/R
D.
P = VI cos(φ)
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Solution
The total power in a series RLC circuit is given by P = VI cos(φ), where φ is the phase angle.
Correct Answer: D — P = VI cos(φ)
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Q. What is the impedance of a series circuit containing a resistor (R) and an inductor (L)?
A.
R
B.
√(R^2 + (ωL)^2)
C.
R + ωL
D.
R - ωL
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Solution
The impedance Z = √(R^2 + (ωL)^2) in a series R-L circuit.
Correct Answer: B — √(R^2 + (ωL)^2)
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Q. What is the impedance of a series circuit containing a resistor and an inductor?
A.
R
B.
√(R^2 + (ωL)^2)
C.
R + jωL
D.
R - jωL
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Solution
The impedance Z in a series R-L circuit is given by Z = √(R^2 + (ωL)^2).
Correct Answer: B — √(R^2 + (ωL)^2)
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Q. What is the impedance of a series RLC circuit at resonance?
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Solution
At resonance, the impedance of a series RLC circuit is equal to the resistance R.
Correct Answer: A — R
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Q. What is the power factor in a circuit with a phase angle of 60 degrees?
A.
0.5
B.
0.866
C.
1
D.
0
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Solution
The power factor is cos(60°) = 0.5.
Correct Answer: B — 0.866
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Q. What is the power factor of a circuit with a phase angle of 60 degrees?
A.
0.5
B.
0.866
C.
1
D.
0.707
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Solution
The power factor (PF) is given by cos(θ). For a phase angle of 60 degrees, PF = cos(60°) = 0.5.
Correct Answer: B — 0.866
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Q. What is the power factor of an AC circuit with a phase angle of 60 degrees?
A.
0.5
B.
0.866
C.
1
D.
0.707
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Solution
The power factor (PF) is given by cos(θ). For a phase angle of 60 degrees, PF = cos(60°) = 0.5.
Correct Answer: B — 0.866
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Q. What is the RMS value of an AC voltage given by V(t) = V0 sin(ωt)?
A.
V0
B.
V0/√2
C.
V0√2
D.
0
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Solution
The RMS value of an AC voltage is given by V_rms = V0/√2.
Correct Answer: B — V0/√2
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Q. What is the root mean square (RMS) value of an alternating current (AC) if its peak value is 10 A?
A.
5 A
B.
7.07 A
C.
10 A
D.
14.14 A
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Solution
The RMS value of an AC is given by I_rms = I_peak / √2. Therefore, I_rms = 10 A / √2 = 7.07 A.
Correct Answer: B — 7.07 A
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Q. What is the root mean square (RMS) value of an alternating current (AC) that has a peak value of 10 A?
A.
5 A
B.
7.07 A
C.
10 A
D.
14.14 A
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Solution
The RMS value of an AC is given by I_rms = I_peak / √2. Therefore, I_rms = 10 A / √2 = 7.07 A.
Correct Answer: B — 7.07 A
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Q. What is the total energy stored in an inductor with inductance L carrying a current I?
A.
LI^2
B.
0.5LI^2
C.
I^2/L
D.
0.5I^2/L
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Solution
The energy stored in an inductor is given by U = 0.5LI^2.
Correct Answer: B — 0.5LI^2
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Q. What is the unit of impedance in an AC circuit?
A.
Ohm
B.
Farad
C.
Henry
D.
Coulomb
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Solution
The unit of impedance in an AC circuit is Ohm, which is the same as resistance.
Correct Answer: A — Ohm
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Q. What is the unit of inductance?
A.
Ohm
B.
Henry
C.
Farad
D.
Coulomb
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Solution
The unit of inductance is Henry (H).
Correct Answer: B — Henry
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